To best understand, let us consider the reactions occurring.
First, we have $\ce{Cl-}$ ions in solution. Acidifying the solution serves to remove other anions that might give a false positive for the chloride test. Upon addition of $\ce{AgNO3}$, the following reaction occurs:
$$\ce{Ag+(aq) +Cl-(aq) -> AgCl (s)}$$
When enough ammonia is added to neutralize the $\ce{H3O+}$ in solution:
$$\ce{NH3(aq) +H3O+(aq) -> NH4+(aq) + H2O(l)}$$
The ammonia can then begin to form a metal complex with the $\ce{AgCl}$ that is soluble in water:
$$\ce{AgCl(s) +2NH3(aq)->Ag(NH3)2+(aq) +Cl-(aq)}$$
When $\ce{HNO3}$ is reintroduced, the ammonia ligand is protonated because it is more basic than water, and the metal complex is destroyed, reforming $\ce{AgCl}$:
$$\ce{Ag(NH3)2+(aq) +2H3O+(aq) +Cl-(aq) ->AgCl(s) +2NH4+(aq) +2H2O(l)}$$
Since you will likely be working with relatively small amounts, it is likely that you will be using concentrated acid in stoichiometric amounts to produce these products.